Bounds on the minimum distance of additive quantum codes

Bounds on [[102,76]]2

lower bound:6
upper bound:8

Construction

Construction of a [[102,76,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[100, 77, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 6, 10, 58, 60, 61, 63, 66, 71, 74, 79, 82, 90, 93, 95, 96, 98, 99, 100, 101, 102, 103, 104, 106, 110, 111, 116, 118, 125 }
[3]:  [[100, 76, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[102, 76, 6]] quantum code over GF(2^2)
     ExtendCode [3] by 2

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0|0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0|0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0|0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0|0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0|0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014